Case Study

The hybrid optimization algorithm was applied on the above-described distribu­tion system.

It is assumed that WTs of three different capacities are chosen by the WT de­velopers. These capacities are 225 kW, 660 kW and 900 kW.

Maximum three WTs of each type are allowed at a given location. This re­quirement may be set by the available land for building WTs. For another distribu­tion network with a different load level, WTs with different capacities may be considered.

Consequently, GA is used to search for the optimal number of WTs of each type at the candidate locations. It is also assumed that the power factor is the same for all WTs connected to the same bus.

The multi-period OPF has been applied for evaluating its annual maximum wind energy exploitation considering the following active management options simultaneously: coordinated OLTC voltage control, energy curtailment and WTs reactive power control.

The basic parameters of the GA are summarized as follows. The total control variables are 33 ( = 3×11), corresponding to the number of three types of WTs at the eleven candidate locations. The population size of each generation is 20. The initial population is generated at random between zero and three.

The GA stops if any of the following conditions is reached:

1) the maximum generation number exceeds 150,

2) there is no improvement in the objective function for 50 consecutive genera­tions, and 3) the cumulative change in the fitness function value over 5 genera­tions is less than 1e-6.

Sensitivity analyses have been carried out to consider different values for the GA parameters such as stop criteria, population size and genetic operators. From these analyses, it was shown that the used values guarantee the convergence of the algo­rithm to a satisfactory solution in this case.

In order to evaluate the effectiveness of the proposed hybrid method, different scenarios for the wind speed distributions in each bus of the network have been assumed.

Table 2 Weibull wind speed distributions parameters

Weibull

distribution

Scale

Parameter

Shape

Parameter

WD1

6

3

WD2

10

3

WD3

18

3

Table 3 Capital costs (Cc) associated to the three candidate WTs

WT Type

Rated output

Capital

Total capital

electric power [kW]

cost [€/kW]

cost [M€]

A

225

1400

0.315

B

660

1200

0.792

C

900

900

0.810

In particular, three different Weibull wind speed distributions have been consi­dered, namely WD1, WD2 and WD3. The corresponding wind power generation have been derived and discretized on the basis of power curves of commercial WTs. The Weibull wind speed distributions parameters are shown in Table 2. Ta­ble 3 lists the capital costs (Cc) associated to the three candidate WTs.

Table 4 NPV for each WT considering the different wind distributions

WT Type

NPV [€]

WD1

WD2

WD3

A

98 320

745 100

1 307 100

B

-264 570

1 964 100

3 958 000

C

-248 600

2 407 500

5 432 200

Table 5 Optimal numbers of WTs at different locations found by the GA and correspond­ing wind speed distribution

Bus

no.

Weibull

distribution

225 kW

660 kW

900 kW

Capacity (kW)

7

WD3

2

1

3

3810

12

WD3

2

1

3

3810

15

WD3

3

0

0

675

29

WD2

2

2

0

1770

26

WD2

1

1

0

885

34

WD3

2

0

2

2250

38

WD3

2

0

2

2250

42

WD3

2

2

3

4470

55

WD1

3

0

0

675

52

WD1

3

0

0

675

62

WD1

1

0

0

225

Total

23

7

13

21495

Table 4 presents the NPV for a single WT of type A, B, and C in correspon­dence of different wind distributions WD1, WD2 and WD2. The negative value of the NPV indicates that the initial investment is higher than the total benefits ob­tained from selling wind power over N years.

It is observed that, under the wind speed distribution of WD3, the investment in a single WT of type C produces higher profits than the investment in one type A WT plus one type B WT. On the contrary, under the wind speed distribution of WD2, the investment in one type A WT plus one type B WT is more beneficial than the investment in one single type C WT.

Moreover, under the wind speed distribution of WD2, the investment in three WTs of type A produces higher profits than the investment in one type B WT. In contrast, under the wind speed distribution of WD3, the investment in one type B WT is more beneficial than the investment in three type A WTs. However, under the wind speed distribution of WD1, only the investment in a type A WT is profitable.

Table 5 lists the optimal numbers of WTs at different locations found by the GA and the corresponding wind speed distribution assumed at each location.

As shown in Table 6 a total WTs capacity of 21.495 MW is installed allowing delivering 126,880 MWh/year, with a curtailed wind energy of 5319 MWh/year.

The total capital cost of the investment is of 23.319 M€ and the NPV equals 108.810 M€.

Table 6 Results of WTs obtained from the hybrid optimisation method

Total

capacity [MW]

Delivered wind ener­gy [MWh]

Total capital cost [M€]

NPV

[M€]

Curtailed wind energy [MWh]

21.495

126 880

23.319

108.820

5319

4 Discussion

The proposed optimization method combines the GA and the multi-period OPF and considers the time-varying characteristics of the load demand and wind power generation. The proposed method allows the WTs developers to optimally allocate a chosen number and types of WTs among a large number of potential combina­tions in an active distribution network. Furthermore, the method can be used to evaluate the feasibility of a project in WTs before carrying out investments. Simu­lation results evidenced that the proposed hybrid method, which maximizes the NPV related to the investment in WTs, is suitable for selecting the optimal site and number of WTs among selected WTs types.

Different active management schemes have been considered in the proposed optimization formulation as they are able to enhance the total amount of wind energy exploitation and thus offer more economic benefits to both WTs develop­ers and DNOs. In fact, active management is expected to provide higher profits to the WTs developers by allowing them connecting more WTs to the network. The active management is also an effective and indispensable strategy for DNOs to in­tegrate and operate WTs in distribution networks and to defer network invest­ments caused by annual load growth and/or DG connections.

Nevertheless, practical implementation of active management schemes requires additional commercial arrangements and financial evaluations. New market rules should be implemented to offer economic benefits to DNOs in order to drive them to provide the active management service to WTs developers. On the other hand, new revenue mechanisms should be developed so that WTs developers and DNOs share the benefits as well as the costs of active management.

Further simulations with larger networks, not presented here, have demonstrat­ed the scalability of the proposed method and its applicability to larger networks [30]. The method is also able to cope with a larger number of control variables [30], [39]. Although this will lead to an increase in the computing time, this is not a constraint as the method is intended for long-term planning studies. Different load profiles (by considering a mix of industrial, commercial and residential cus­tomers) for each node can be easily introduced in the method.

The main drawback of the proposed hybrid optimization algorithm is that the simu­lation time is very long. This is due to the evaluation of the fitness function which each time calls for a lengthy multi-period OPF. However, this drawback can be tolerated as simulation time is not a major concern for long-term system planning. In addition, a more powerful computer may improve the simulation speed to a certain extent.

5 Conclusion

This chapter has described a hybrid optimization method that can help WTs de­velopers to plan investments in an active distribution network. The hybrid optimi­zation method, combining the GA and the multi-period OPF, maximizes the NPV related to the investment in WTs and allows evaluating the economic benefits de­riving from active management schemes. Simulation results on a 69-bus 11 kV radial distribution network confirmed the effectiveness of the proposed method in selecting the optimal site and number of WTs among different WTs types.

1. (1997)

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